I described Pandora giving Edward his first spell as "convenient". One reason for that is because it helps keep part of this first meeting with Hope brief:

The matter of Hope proving her identity to Edward.

Without such assistance, it would have been entirely in-character for Edward to turn this into a "prove who you are" interrogation.

While it's true her being a "guest" would be decent enough reason to not feel too threatened, it wouldn't guarantee a total lack of deception.

Speaking of hospitality...

How he can see the room

Here is the simple explanation for why Edward can see the room. The room is hidden on a basis of hospitality, and this is Edward's home. Not only does that mean he can see and enter the room, Hope could only put the entrance there because she was an invited guest.

As for the entrance in the comic shop, no one actually lives there, so Hope was able to just make the entrance without permission.

As Hope has mentioned, this is a "what the person believes" situation, so these are not universal truths for immortals. It would be a very rare immortal who could ignore the rules of hospitality in someone's home, should any exist at all, but an overly courteous immortal might extend considerations of hospitality to a place of business.

In fact, the type of business could matter. A family-owned restaurant, for example, could easily affect someone's honest interpretation of the rules.

Nothing's REALLY canon until it's in the comic itself, of course (if for no other reason than I might wind up changing my mind and contradicting myself), but I'm still going to claim that Hope herself would consider the rules of hospitality applicable to a family-owned restaurant.

Perhaps Pandora offered Hospitality?

After the first page of this arc was posted, I saw a few people theorize that, long ago, Pandora herself offered Edward Hospitality. This couldn't have been the answer, but that's for reasons that have not been stated, so no one was missing anything.

One reason is simply the separation of Pandora and Hope. Hope would not be obligated to honor offers of hospitality made by Pandora unless those were special offers made under special circumstances.

Another is that, unless Hope is offering to let someone be a long term guest, or a resident in some capacity, offers of hospitality aren't indefinite. A welcomed guest is a guest for a duration, such as the length of a visit. Such a limit generally doesn't have to be spelled out, either, as social conventions will usually be expected and understood.

Which makes sense, really. If you've invited your buddy Steve over to watch a movie at your home one night, that doesn't mean they're now free to come over any time they want.

WE HAVE TO SET BOUNDARIES, STEVE